A dynamic process model of skill acquisition in elementary mathematics that can accommodate individual differences is proposed. Four factors governing skill acquisition were identified and include the development of; (l) counting knowledge; (2) skill at using counting algorithms to solve arithmetic problems; (3) long-term memory representations of number facts; and, (4) working memory resources. The process model represents the dynamic relationships among these factors and serves as the basis for design of the proposed studies. Experiment 1 will provide a comprehensive longitudinal assessment of the development of each of these four skills for groups of normal and mathematically disabled (MD) children, and a comprehensive neuropsychological assessment of the numerical skills of individual MD children. Experiment 2 will test the hypothesis that cross-cultural differences in the learning of elementary mathematics are related to national differences in numerical working memory resources and mathematics instruction. Finally, a computational system, following the production-system framework, of the process model will be refined so that individual differences in skill acquisition can be modeled. These experiments will enable an empirical test of hypotheses generated by the process model and at the same time provide invaluable information on the source of mathematical ability and achievement differences in children. Empirical verification of the model will greatly advance our understanding of the development of number skills in children, because the model subsumes extant developmental models (e.g., the strategy choice model) and can accommodate individual differences, whether the differences are manifested as a mathematical disability, or multinational achievement differences. More practically, these studies will provide a solid foundation from which sensitive techniques for the assessment and early identification of mathematical learning problems could be developed. Such techniques should help to identify the locus of the learning problem and therefore could lead to the development of more effective remedial education programs in mathematics. Finally, the studies will provide unique information on the components of mathematical skill that most sharply differentiate the achievement of East Asian and American children. These, in turn, could be targets for mathematics education in the United States.